Pach and Sharir [1]} proved that, for all \(0<þ<\pi \) , any set of \(n\)  points in the Euclidean plane contains at most \(O(n^2\log n)\)  triples which determine an angle with measure \(þ\) . They also showed that, for \(\tan (þ)=\frac{am}{b}\)  with \(a,b,m\)  positive integers, this upper bound is tight, and that there exists a configuration of \(n\)  points in the plane with \(\Omega _þ(n^2\log n)\)  triples determining angle \(þ\) . However, for other \(þ\) , it remains open whether the upper bound is asymptotically tight (see problem 6, Chapter 6.2 in [2]}).
